Related papers: Noise and slow-fast dynamics in a three-wave reson…

We study the effects of noise cross-correlations on the steady states of driven, nonequilibrium systems, which are described by two stochastically driven dynamical variables, in one dimension. We use a well-known stochastically driven…

Based on the physics of stochastic processes we present a new approach for structural health monitoring. We show that the new method allows for an in-situ analysis of the elastic features of a mechanical structure even for realistic…

The dynamic response of a gas bubble entrapped in a cavity on the surface of a submerged solid subject to an acoustic field is investigated in the linear approximation. We derive semi-analytical expressions for the resonance frequency,…

This article reports on a new approach to properly analyze time series of dynamical systems which are spoilt by the simultaneous presence of dynamical noise and measurement noise. It is shown that even strong external measurement noise as…

The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…

A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular perturbation theory and numerical continuation. Two types of…

Quantum noise in a model of singly resonant frequency doubling including phase mismatch and driving in the harmonic mode is analyzed. The general formulae about the fixed points and their stability as well as the squeezing spectra…

We study a family of dynamical systems obtained by coupling an Anosov map on the two-dimensional torus -- the chaotic system -- with the identity map on the one-dimensional torus -- the neutral system -- through a dissipative interaction.…

Opposition flow control is a robust strategy that has been proved effective in turbulent wall-bounded flows. Its conventional setup consists of measuring wall-normal velocity in the buffer layer and opposing it at the wall. This work…

Industrial coating processes create thin liquid films with tight thickness tolerances, and thus models that predict the response to inevitable disturbances are essential. The mathematical modeling complexities are reduced through…

There are many problems that lead to analysis of dynamical systems in which one can distinguish motions of two types: slow one and fast one. An averaging over fast motion is used for approximate description of the slow motion. First…

We consider a slow-fast Hamiltonian system with one fast angular variable (a fast phase) whose frequency vanishes on some surface in the space of slow variables (a resonant surface). Systems of such form appear in the study of dynamics of…

We study the role played by noise on the QW introduced in [1], a 1D model that is inspired by a two particle interacting QW. The noise is introduced by a random change in the value of the phase during the evolution, from a constant…

We present a simple dynamical model to address the question of introducing a stochastic nature in a time variable. This model includes noise in the time variable but not in the "space" variable, which is opposite to the normal description…

We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and disclose a novel noise-induced ordering phenomenon. For long unstable periodic orbits forming the strange attractor the weights (or…

Computation plays a key role in predicting and analyzing natural phenomena. There are two fundamental barriers to our ability to computationally understand the long-term behavior of a dynamical system that describes a natural process. The…

We consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems, where the character of the bifurcation changes from sub- to supercritical behaviour. Starting from a general…

During the last decades active particles have attracted an incipient attention as they have been observed in a broad class of scenarios, ranging from bacterial suspension in living systems to artificial swimmers in nonequilibirum systems.…

In this tutorial, three examples of stochastic systems are considered: A strongly-damped oscillator, a weakly-damped oscillator and an undamped oscillator (integrator) driven by noise. The evolution of these systems is characterized by the…

In this article, the dynamics and complexity of a noise induced blood flow system have been investigated. Changes in the dynamics have been recognized by measuring the periodicity over significant parameters. Chaotic as well as non-chaotic…